It is proved that for a smooth compactification of a quotient space of a linear space by the action of a linear algebraic group , the Artin-Mumford birational invariant is effectively computable in terms of the 2-dimensional group cohomology of ; examples of groups for which the invariant is nontrivial are also studied. Bibliography: 6 titles.
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Fedor Alekseevich Bogomolov (1988) studied this question.
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